Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
884 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64078 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 4. #11722031 | C2 | semidirect |
| 16. #64078 | D3 | semidirect |
| 142. C33 | #486 | semidirect |
| 207. C32 | #5070 | semidirect |
| 208. C32 | #5088 | semidirect |
| 239. C3 | #10590277 | semidirect |
| 240. C3 | #10592769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64078 | 2 |
| C32×#874 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722031 | 2 |
| #10592769 | 3 |
| #10590277 | 3 |